Problem: is 5x - 8y= -25 and 2x - 9y= -39 a solution
is this a soultion
No, it is just a system of two equations. You need
to solve them simultaneously to arrive at a solution.
5x - 8y = -25
2x - 9y = -39
9(5x - 8y) = -25 * 9
45x - 72y = -225
8(2x - 9y) = -39 * 8
16x - 72y = -312
The overall values of the two equations have not changed,
only the way they are presented has changed. However, you
now have two equations with the same co-efficient for y.
Subtract one equation from the other.
45x - 72y = -225
-(16x - 72y = -312)
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29x = 87
29x = 87
29x/29 = 87/29
x = 3
Use that to solve for y in the first equation.
5x - 8y = -25
5(3) - 8y = -25
15 - 8y = -25
15 - 8y - 15 = -25 - 15
-8y = -40
-8y/-8 = -40/-8
y = 5
Use the second equation to check your work.
2x - 9y = -39
2(3) - 9(5) = -39
6 - 45 = -39
-39 = -39
Answer: x = 3, y = 5
Now THAT'S a solution!